Discussiones Mathematicae Graph Theory 27(3) (2007)
409-423
doi: 10.7151/dmgt.1371
ROBERT R. RUBALCABA^{1} AND PETER J. SLATER^{1,2}
^{1}Department of Mathematical Sciences
University of Alabama in Huntsville
Huntsville, AL 35899, USA
e-mail: r.rubalcaba@gmail.com
^{2}Department of Computer Science
University of Alabama in Huntsville
Huntsville, AL 35899, USA
e-mail: slater@math.uah.edu
Keywords: efficient domination, multiple domination.
2000 Mathematics Subject Classification: 05C69.
[1] | D.W. Bange, A.E. Barkauskas and P.J. Slater, Disjoint dominating sets in trees, Sandia Laboratories Report, SAND 78−1087J (1978). |
[2] | D.W. Bange, A.E. Barkauskas and P.J. Slater, Efficient dominating sets in graphs, in: R.D. Ringeisen and F.S. Roberts (eds.) Applications of Discrete Mathematics, pages 189-199, (SIAM, Philadelphia, PA, 1988). |
[3] | D.W. Bange, A.E. Barkauskas and P.J. Slater, Efficient near-domination of grid graphs, Congr. Numer. 58 (1986) 83-92. |
[4] | D.W. Bange, A.E. Barkauskas, L.H. Host and P.J. Slater, Generalized domination and efficient domination in graphs, Discrete Math. 159 (1996) 1-11, doi: 10.1016/0012-365X(95)00094-D. |
[5] | N. Biggs, Perfect codes in graphs, J. Combin. Theory (B) 15 (1973) 288-296, doi: 10.1016/0095-8956(73)90042-7. |
[6] | M. Chellali, A. Khelladi and F. Maffray, Exact double domination in graphs, Discuss. Math. Graph Theory 25 (2005) 291-302, doi: 10.7151/dmgt.1282. |
[7] | G.S. Domke, S.T. Hedetniemi, R.C. Laskar and G. Fricke, Relationships between integer and fractional parameters of graphs, in: Y. Alavi, G. Chartrand, O.R. Oellermann and A.J. Schwenk (eds.), Graph Theory, Combinatorics, and Applications, Proceedings of the Sixth Quadrennial International Conference on the Theory and Applications of Graphs, vol. 1, pages 371-387, (Kalamazoo, MI 1988), Wiley Publications, 1991. |
[8] | M. Farber, Domination, independent domination, and duality in strongly chordal graphs, Discrete Appl. Math. 7 (1984) 115-130, doi: 10.1016/0166-218X(84)90061-1. |
[9] | J.F. Fink and M.S. Jacobson, n-domination in graphs, in: Graph Theory with Applications to Algorithms and Computer Science (Wiley, New York, 1984) 283-300. |
[10] | W. Goddard and M.A. Henning, Real and integer domination in graphs, Discrete Math. 199 (1999) 61-75, doi: 10.1016/S0012-365X(98)00286-6. |
[11] | D.L. Grinstead and P.J. Slater, On the minimum intersection of minimum dominating sets in series-parallel graphs, in: Y. Alavi, G. Chartrand, O.R. Oellermann and A.J. Schwenk (eds.), Graph Theory, Combinatorics, and Applications, Proceedings of the Sixth Quadrennial International Conference on the Theory and Applications of Graphs, vol. 1, pages 563-584, (Kalamazoo, MI 1988), Wiley Publications, 1991. |
[12] | D.L. Grinstead and P.J. Slater, Fractional domination and fractional packing in graphs, Congr. Numer. 71 (1990) 153-172. |
[13] | F. Harary and T.W. Haynes, Nordhaus-Gaddum inequalities for domination in graphs, Discrete Mathematics 155 (1996) 99-105, doi: 10.1016/0012-365X(94)00373-Q. |
[14] | R.R. Rubalcaba and M. Walsh, Minimum fractional dominating and maximum fractional packing functions, submitted. |
[15] | R.R. Rubalcaba and P.J. Slater, A note on obtaining k dominating sets from a k-dominating function on a tree, submitted. |
[16] | P.J. Slater, Generalized graph parameters: Gallai theorems I, Bull. Inst. of Comb. Appl. 17 (1996) 27-37. |
Received 1 April 2006
Revised 16 May 2007
Accepted 16 May 2006